1. The problem is to graph the piecewise function: $$f(x) = \begin{cases} 2x - 1 & \text{if } x < 0 \\ -1 & \text{if } x \geq 0 \end{cases}$$ 2. For $x < 0$, the function is a line with equation $y = 2x - 1$. - To graph this, pick points like $x = -1$, $f(-1) = 2(-1)-1 = -3$. - Another point is $x = -2$, $f(-2) = 2(-2)-1 = -5$. 3. For $x \geq 0$, the function is constant $y = -1$. - This means a horizontal line at $y = -1$ starting at $x=0$ and extending right. 4. At $x=0$, the function value is $f(0) = -1$ (included in the horizontal line). 5. Plot the left piece as a line through points $(-2, -5)$ and $(-1, -3)$ extending up to but not including $x=0$. 6. Plot the right piece as a horizontal line at $y=-1$ starting at $x=0$ (solid point) and extending to the right. Final graph is a piecewise function with a line declining to the left of zero and a flat line at $-1$ at zero and beyond.